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Type: Artigo de periódico
Author: Carnielli, W
Carolino, PK
Abstract: We investigate a conjecture of Paul Erdos, the last unsolved problem among those proposed in his landmark paper [2]. The conjecture states that there exists an absolute constant C > 0 such that, if, v are unit vectors in a Hilbert space, then at least C2(n)/n of all epsilon is an element of {-1, 1}(n) are such that vertical bar Sigma(n)(i=1) epsilon(i)v(i) vertical bar <= 1. We disprove the conjecture. For Hilbert spaces of dimension d > 2, the counterexample is quite strong, and implies that a substantial weakening of the conjecture is necessary. However, for d = 2, only a minor modification is necessary, and it seems to us that it remains a hard problem, worthy of Erdos. We prove some weaker related results that shed some light on the hardness of the problem.
Subject: Erdos conjecture
Littlewood-Offord reverse problem
Country: Canadá
Editor: Univ Calgary, Dept Math & Statistics
Citation: Contributions To Discrete Mathematics. Univ Calgary, Dept Math & Statistics, v. 6, n. 1, n. 154, n. 159, 2011.
Rights: aberto
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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